Step-by-step explanation:

In general, water harvesting is the activity of the direct collection of rainwater. The rainwater collected can be stored for direct use or can be recharged into the groundwater. Rain is the first form of water that we know in the hydrological cycle, hence is a primary source of water for us. It is also the infiltration of surface water into subsurface aquifers (before it is lost as surface runoff).

Concept

The volume of a cylinder with base radius "r" and height "h" is V = πr^2 h. If the diameter of its base is d, then we have d = r/2.

Given

Rajkumar has a roof with dimensions shown. He knows that the average rainfall in his suburb is 77 cm per year. Rajkumar would like to install a underground cylindrical rain water tank to hold the water that runs off the roof.

Find

We need to find (i) On average what volume of water will fall on the roof each year? (ii) If the tank has base diameter 7 m, how deep it need to be?

Solution

Let 5=s

and l^2 + s^2 = 13^2

l^2 + 5^2 = 13^2

l^2=169-24

l^2 = 144

l= 12

On average what volume of water will fall on the roof each year=2l * 50 =2*12 +50

= 24 *50

=1200m^2

If the tank has base diameter 7m then r=d/2 =7/2 m

Rajkumar knows that the average rainfall in his suburb is 77 cm per year=0.77 m per year

V=L*B*H=1200 *0.77= 924 m^2

then, πr^2 h= 924

22/7 * 7/2 * 7/2 * h = 924

h = 924*7*2*2/22*7*7

h = 24 m

Hence on average what volume of water will fall on the roof each year is 1200 m^2 and if the tank has base diameter 7 m, then it is 24 m deep

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